084707-2 Hocker et al. J. Chem. Phys. 136, 084707 (2012) II. FORCE FIELD GENERATION A. Tangney-Scandolo force field The TS force field is a sum of two contributions: a shortrange pair potential of Morse-Stretch (MS) form, and a longrange part, which describes the electrostatic interactions between charges and induced dipoles on the oxygen atoms. The MS interaction between an atom of type i and an atom of type j has the form ( )] [ ( )]] Uij MS = D ij [exp [γ ij 1 − r ij γ ij rij 0 − 2exp 1 − r ij 2 rij 0 with r ij =|r ij |, r ij = r j − r i and the model parameters D ij , γ ij , and rij 0 , which have to be determined during the force field generation. Because the dipole moments depend on the local electric field of the surrounding charges and dipoles, a self-consistent iterative solution has to be found. In the TS approach, a dipole moment p n i at position r i in iteration step n consists of an induced part due to an electric field E(r i ) and a short-range part p SR i due to the short-range interactions between charges q i and q j . Following Rowley et al., 21 this contribution is given by ∑ p SR q j r ij i = α i rij 3 f ij (r ij ) (2) with f ij (r ij ) = c ij j≠i (1) 4∑ (b ij r ij ) k e −b ij r ij . (3) k! k=0 b ij and c ij are parameters of the model. Together with the induced part, one obtains p n i = α i E ( r i ; { p n−1 j }j=1,N , {r ) j } j=1,N + p SR i , (4) where α i is the polarizability of atom i and E(r i ) is the electric field at position r i , which is determined by the dipole moments p j in the previous iteration step. Taking into account the interactions between charges U qq , between dipole moments U pp and between a charge and a dipole U pq ,thetotal electrostatic contribution is given by and the total interaction is B. Wolf summation U EL = U qq + U pq + U pp , (5) U tot = U MS + U EL . (6) The electrostatic energies of a condensed system are described by functions with r −n dependence, n ∈ {1,2,3}.For point charges (r −1 ), it is common to apply the Ewald method, where the total Coulomb energy of a set of N ions, E qq = 1 2 N∑ i=1 N∑ j=1 j≠i q i q j r ij , (7) is decomposed into two terms Er qq and E qq k by inserting a unity of the form 1 = erfc(κr) + erf(κr) with the error function erf(κr) := √ 2 ∫ κr dt e −t 2 . (8) π The splitting parameter κ controls the distribution of energy between the two terms. The short-ranged erfc term is summed up directly, while the smooth erf term is Fourier transformed and evaluated in reciprocal space. This restricts the technique to periodic systems. However, the main disadvantage is the scaling of the computational effort with the number of particles in the simulation box, which increases as O(N 3/2 ), 22 even for the optimal choice of κ. Wolf et al. 17 designed a method with linear scaling properties O(N) for Coulomb interactions. By taking into account the physical properties of the system, the reciprocal-space term E qq k is disregarded. It can be written as E qq k = 2π V ∑ k≠0 |k|